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| 1 : | jj | 248 | ##DESCRIPTION |
| 2 : | ##ENDDESCRIPTION | ||
| 3 : | ## Edited Z. Song, Union College, 9/7/03 | ||
| 4 : | |||
| 5 : | DOCUMENT(); # This should be the first executable line in the problem. | ||
| 6 : | |||
| 7 : | loadMacros( | ||
| 8 : | "PG.pl", | ||
| 9 : | "PGbasicmacros.pl", | ||
| 10 : | "PGchoicemacros.pl", | ||
| 11 : | "PGanswermacros.pl", | ||
| 12 : | "PGauxiliaryFunctions.pl", | ||
| 13 : | "PGunion.pl", # Union College utilities | ||
| 14 : | "PGcourse.pl", # Customization file for the course | ||
| 15 : | ); | ||
| 16 : | |||
| 17 : | TEXT(beginproblem()); | ||
| 18 : | BEGIN_PROBLEM(); | ||
| 19 : | |||
| 20 : | $a = non_zero_random(-4,4,1); | ||
| 21 : | $b = non_zero_random(-5,5,1); | ||
| 22 : | $expa = $a-1; | ||
| 23 : | |||
| 24 : | $df = "[${a}x^($expa)]sec($b/x)+x^($a)*[sec($b/x)tan($b/x)*(-$b/x^2)]"; | ||
| 25 : | |||
| 26 : | BEGIN_TEXT | ||
| 27 : | Suppose that \( f(x) = x^{$a}\sec\left( \displaystyle \frac{$b}{x} \right) \). | ||
| 28 : | Find \(f'(x)\). | ||
| 29 : | $PAR | ||
| 30 : | \(f'(x)\) = \{ans_rule(60)\}. | ||
| 31 : | END_TEXT | ||
| 32 : | |||
| 33 : | $showPartialCorrectAnswers=1; | ||
| 34 : | |||
| 35 : | ANS(fun_cmp( | ||
| 36 : | $df, # the correct answer | ||
| 37 : | limits => [.1,1], # range of x's to use | ||
| 38 : | relTol => .1, # .1 percent, (i.e., .001) | ||
| 39 : | )); | ||
| 40 : | |||
| 41 : | ################################################## | ||
| 42 : | |||
| 43 : | END_PROBLEM(); | ||
| 44 : | ENDDOCUMENT(); # This should be the last executable line in the problem. |
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